A novel algorithm developed within muon radiography to localize objects or cavities hidden inside large material volumes was recently proposed by some of the authors (Bonechi 2015 , P02003 (doi:10.1088/1748-0221/10/02/P02003)). The algorithm, based on muon back projection, helps to estimate the three-dimensional position and the transverse extension of detected objects without the need for measurements from different points of view, which would be required to make a triangulation. This algorithm can now be tested owing to the availability of real data collected both in laboratory tests and from real-world measurements. The methodology and some test results are presented in this paper.This article is part of the Theo Murphy meeting issue 'Cosmic-ray muography'.